Surface Mesh Generation for Generalized FEM-Techniques

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Established approaches for (surface) domain discretization usually aim to generate tessellations of the underlying surface consisting of triangles or quadrilaterals (or mixtures of both) since these are compatible with standard FEM basis functions. The generalized discretization techniques that will be investigated in this research group, however, allow for more flexibility with respect to the (local) shape of the individual cells as well as the (global) structure of the overall mesh. Since, e.g., SBFEM and VEM methods can deal with arbitrary convex or star-shaped polygonal cells, they provide more flexibility concerning the adjustment of the cells, their alignment to relevant structures, as well as their (anisotropic) sizing. In this sub-project we will systematically explore these additional degrees of freedom in mesh generation for freeform surfaces and develop novel techniques for the efficient and flexible generation of polygonal cell decompositions with controllable properties. We aim at developing efficient and flexible mesh generation techniques that take into account the specific restrictions and exploit the added freedom of generalized discretization approaches. In particular, we will systematically explore properties such as (1) varying size, anisotropy, and shape of cells, (2) mesh adaptivity without local refinement by shifting existing nodes into regions that require finer resolution and (3) enforcing unconditional ("built-in") cell planarity for shells. By developing flexible meshing schemes that enable the efficient update of the mesh structure or vertex distribution, the simulation and meshing stages of a computational analysis process can be interleaved and integrated for optimal performance.